I didn't notice that prime factorization of n^2 can be reduced to a slightly modified prime factorization of n.
Thanks to www.mathblog.dk/project-euler-108-diophantine-equation/ where I found that trick (see numSquareDivisors)
The code becomes much faster but I kept my old code numDivisors for the original problem.

However, I still time-out on two thirds of the test cases (my old code timed out in 80% of all cases).

Interactive test

You can submit your own input to my program and it will be instantly processed at my server:

This live test is based on the Hackerrank problem.

Number of test cases (1-5):

Input data (separated by spaces or newlines):Note: Enter n and the program will compute the number of solutions

This is equivalent toecho "1 3" | ./108

Output:

(please click 'Go !')

(this interactive test is still under development, computations will be aborted after one second)

My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too.

The code contains #ifdefs to switch between the original problem and the Hackerrank version.Enable #ifdef ORIGINAL to produce the result for the original problem (default setting for most problems).

#include<iostream>

//#define ORIGINAL

// count divisors

unsignedlonglongnumDivisors(unsignedlonglong n)

{

unsignedint result = 1;

auto reduce = n;

// trial division by all prime numbers

// => I didn't precompute a sieve, therefore divide by 2 and all odd numbers

for (unsignedlonglong divisor = 2; divisor <= reduce; divisor++)

{

// 2 is the only even prime number

if (divisor % 2 == 0 && divisor > 2)

divisor++;

if (divisor > 100) // WARNING: unsafe speed optimization !

break; // returns correct values for original problem but fails for some Hackerrank test cases

unsignedint exponent = 0;

while (reduce % divisor == 0)

{

exponent++;

reduce /= divisor;

}

result *= exponent + 1;

}

return result;

}

// count divisors of n^2, note: parameter is n, not n^2 (this is different from my old code in numDivisors)

unsignedlonglongnumSquareDivisors(unsignedlonglong n)

{

unsignedint result = 1;

auto reduce = n;

// trial division by all prime numbers

// => I didn't precompute a sieve, therefore divide by 2 and all odd numbers

for (unsignedlonglong divisor = 2; divisor <= reduce; divisor++)

{

// 2 is the only even prime number

if (divisor % 2 == 0 && divisor > 2)

divisor++;

unsignedint exponent = 0;

while (reduce % divisor == 0)

{

exponent++;

reduce /= divisor;

}

result *= 2*exponent + 1; // changed vs. my code: times 2

}

return result;

}

intmain()

{

#ifdef ORIGINAL

unsignedlonglong n = 1;

unsignedlonglong threshold = 1000;

while (true)

{

auto divisors = numDivisors(n * n);

// a and b are interchangeable therefore only half of the solutions are "unique"

Hackerrank

Difficulty

30%
Project Euler ranks this problem at 30% (out of 100%).

Hackerrank describes this problem as easy.

Note:Hackerrank has strict execution time limits (typically 2 seconds for C++ code) and often a much wider input range than the original problem.In my opinion, Hackerrank's modified problems are usually a lot harder to solve. As a rule thumb: brute-force is rarely an option.

Those links are just an unordered selection of source code I found with a semi-automatic search script on Google/Bing/GitHub/whatever.
You will probably stumble upon better solutions when searching on your own.
Maybe not all linked resources produce the correct result and/or exceed time/memory limits.

Heatmap

Please click on a problem's number to open my solution to that problem:

green

solutions solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too

yellow

solutions score less than 100% at Hackerrank (but still solve the original problem easily)

gray

problems are already solved but I haven't published my solution yet

blue

solutions are relevant for Project Euler only: there wasn't a Hackerrank version of it (at the time I solved it) or it differed too much

orange

problems are solved but exceed the time limit of one minute or the memory limit of 256 MByte

red

problems are not solved yet but I wrote a simulation to approximate the result or verified at least the given example - usually I sketched a few ideas, too

black

problems are solved but access to the solution is blocked for a few days until the next problem is published

[new]

the flashing problem is the one I solved most recently

I stopped working on Project Euler problems around the time they released 617.

The 310 solved problems (that's level 12) had an average difficulty of 32.6&percnt; at Project Euler and
I scored 13526 points (out of 15700 possible points, top rank was 17 out of &approx;60000 in August 2017)
at Hackerrank's Project Euler+.

My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.

Copyright

I hope you enjoy my code and learn something - or give me feedback how I can improve my solutions.All of my solutions can be used for any purpose and I am in no way liable for any damages caused.You can even remove my name and claim it's yours. But then you shall burn in hell.

The problems and most of the problems' images were created by Project Euler.Thanks for all their endless effort !!!

more about me can be found on my homepage,
especially in my coding blog.
some names mentioned on this site may be trademarks of their respective owners.
thanks to the KaTeX team for their great typesetting library !